Pessimistic Optimal Choice for Risk-Averse Agents: The Continuous-Time Limit

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• 作者：Paolo Vitale
• 关键词：Pessimistic agents ; Time ; discounting ; Linear exponential quadratic Gaussian
• 刊名：Computational Economics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：49
• 期：1
• 页码：17-65
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Economic Theory/Quantitative Economics/Mathematical Methods; Computer Appl. in Social and Behavioral Sciences; Operation Research/Decision Theory; Behavioral/Experimental Economics; Math Applications
• 出版者：Springer US
• ISSN：1572-9974
• 卷排序：49

文摘

We extend Hansen and Sargent’s (Discounted linear exponential quadratic gaussian control, 1994, IEEE Trans Autom Control 40:968–971 1995, 2013) analysis of dynamic optimization with risk-averse agents in two directions. Firstly, following Whittle (Risk-sensitive optimal control, 1990), we show that the optimal risk-averse policy is identified via a pessimistic choice mechanism and described by simple recursive formulae. Secondly, we investigate the continuous-time limit and show that sufficient conditions for the existence of optimal solutions coincide with those which apply under risk-neutrality. Our analysis is conducted both under perfect and imperfect state observation. As an illustrative example, we analyze the optimal production policy of an entrepreneur running a monopolistic firm which faces a demand schedule subject to stochastic shocks, showing that risk-aversion induces her to act more aggressively.